Voter models on subcritical inhomogeneous random graphs

Por • 6 dic, 2019 • Sección: Ciencia y tecnología

John Fernley, Marcel Ortgiese

The voter model is a classical interacting particle system modelling how consensus is formed across a network. We analyse the time to consensus for the voter model when the underlying graph is a subcritical scale-free random graph. Moreover, we generalise the model to include a `temperature’ parameter. The interplay between the temperature and the structure of the random graph leads to a very rich phase diagram, where in the different phases different parts of the underlying geometry dominate the time to consensus. Finally, we also consider a discursive voter model, where voters discuss their opinions with their neighbours. Our proofs rely on the well-known duality to coalescing random walks and a detailed understanding of the structure of the random graphs.

arXiv:1911.13187v1 [math.PR]

Probability (math.PR)

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